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StatTutor Lesson - Measuring Spread: the Standard Deviation

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Measuring spread-the standard deviation 6ed
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      Questions 1-2

      36

      Question 1.

      Which measures are the same for the two data sets?

      A.
      B.

      Correct. Both histograms are centered at the same place.
      Incorrect. Both histograms are centered at the same place.
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      Questions 3-4

      66

      Question 3.

      Which measures are the same for the two data sets?

      A.
      B.

      Correct. The histograms are both centered at the same place.
      Incorrect. The histograms are both centered at the same place.
      2
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      Questions 5-6

      183

      Question 5.

      Fill in the blank: The deviation for each observation is computed by _______________ the observation.

      A.
      B.
      C.
      D.

      Correct. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, ¯x.
      Incorrect. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, ¯x.
      2
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      Question 7

      241

      Question 7.

      What is the symbol for sample standard deviation?

      A.
      B.
      C.

      Correct. “s” is the symbol for sample standard deviation.
      Incorrect. “s” is the symbol for sample standard deviation.
      2
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      Questions 8-9

      368

      Question 8.

      Graphically, how is variance represented?

      A.
      B.
      C.

      Correct. Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.
      Incorrect.Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.
      2
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      Questions 10-11

      387

      Question 10.

      True or false: Standard deviation, s, has the same unit of measure as the data.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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      Question 12

      544

      Question 12.

      How do you think is the best way to compute standard deviation?

      A.
      B.

      Correct. No one likes to spend time computing standard deviation by hand.
      Incorrect. No one likes to spend time computing standard deviation by hand.
      2
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      Applet

      559

      Questions 13-17

      612

      Question 13.

      Can standard deviation be negative?

      A.
      B.

      Correct. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.
      Incorrect. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.
      2
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      Question 18

      688

      Question 18.

      True or false: We always divide by “n” when computing sample standard deviation.

      A.
      B.

      Correct. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.
      Incorrect. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.
      2
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      Question 19

      724

      Question 19.

      What is the biggest problem with sample standard deviation?

      A.
      B.
      C.
      D.

      Correct. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.
      Incorrect. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.
      2
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      Question 20

      837

      Question 20.

      For these data, what is the range?

      A.
      B.
      C.
      D.

      Correct. range = maximum minus minimum = 47 – 34 = 13
      Incorrect. range = maximum minus minimum = 47 – 34 = 13
      2
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      Question 21

      857

      Question 21.

      Which value is a good estimate of the standard deviation for these data?

      A.
      B.
      C.
      D.

      Correct. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.
      Incorrect. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.
      2
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      Question 22

      914

      Question 22.

      Which value is a good estimate of the standard deviation for these data?

      A.
      B.
      C.
      D.

      Correct. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.
      Incorrect. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.
      2
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      Question 23

      971

      Question 23.

      Fill in the blank: The standard deviation including the seven extreme values will be ______________ the standard deviation computed without the seven values.

      A.
      B.
      C.

      Correct. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.
      Incorrect. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.
      2
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      Question 24

      1037

      Question 24.

      Where would you choose to live if you want a stable climate with low variability in temperature?

      A.
      B.

      Correct. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.
      Incorrect. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.
      2
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      Question 25

      1074

      Question 25.

      Which mutual fund would you choose if you are a risk taker and want to try to get the highest possible percent return?

      A.
      B.

      Correct. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.
      Incorrect. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.
      2
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